Buys-Ballot Estimates for Linear Model with the Expected Values in Time Series Decomposition

The study discusses the Buys-Ballot estimates for linear trend-cycle and seasonal indices with the expected values for mixed model in time series analysis. The emphasis is to derive the expected values of row, column and overall means of the of Buys-Ballot table for the mixed model. We use a real life data to determine the estimation of trend parameters, seasonal indices and choice of appropriate model of the Buys-Ballot table. Results indicate that, (1) the expected value of the row average mimic the shape of the trending parameters of the original series and contains seasonal effect in \[C_1=\sum_{j=1}^S j s_j\] (2) the expected value of the column average also mimic the shape of the trending curves of the original series and contain seasonal effect (3) the appropriate model that best describe the pattern of the study series listed in the summary table (Table 5) is mixed.